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Determine the value of each variable. Enter your answers as decimals. x = Blank #1 y = Blank #2 z = Blank #3 Question 1 options: Blank # 1 Blank # 2 Blank # 3

Determine the value of each variable. Enter your answers as decimals. x = Blank #1 y = Blank #2 z = Blank #3 Question 1 options: Blank # 1 Blank # 2 Blank # 3 class=

Answer :

kudzordzifrancis

Answer:

x=31.25°

y=49.5°

z=130.5°

Step-by-step explanation:

From the diagram, z° corresponds to

[tex] (\frac{6}{5}x + 10) \degree[/tex]

and

[tex](2x - 13) \degree[/tex]

This implies that

[tex]z = (\frac{6}{5}x + 10) \degree[/tex]

and

[tex]z = (2x - 13) \degree[/tex]

[tex] \implies \: (\frac{6}{5}x + 10) \degree = (2x - 13) \degree[/tex]

Multiply through by 5:

[tex]6x + 50 = 10x - 65[/tex]

Group similar terms:

[tex]50 + 65 = 10x - 6x[/tex]

[tex]125 = 4x[/tex]

[tex]x = \frac{125}{4} [/tex]

[tex]x = 31.25 \degree[/tex]

[tex] \implies \: z = 2 \times 31.25 - 13 = 49.5 \degree[/tex]

Angles on straight line are supplementary

[tex]y + z = 180[/tex]

[tex]49.5 + z = 180[/tex]

[tex]z = 180 - 49.5 = 130.5 \degree[/tex]

When two lines are Parallel

1.Corresponding Angles are equal.

2.Alternate interior angles are equal.

3. Sum of interior angle on the same side of transversal is 180°.

[tex]1.\frac{6x}{5}+10^{\circ}+y^{\circ}=180^{\circ}\\\\y=170^{\circ}-\frac{6x}{5}\\\\2.y^{\circ}+z^{\circ}=180^{\circ}\\\\z^{\circ}=(2x-13)^{\circ}\\\\y^{\circ}+(2x-13)^{\circ}=180^{\circ}\\\\170^{\circ}-\frac{6x}{5}+(2x-13)^{\circ}=180^{\circ}\\\\ \frac{4x}{5}=10^{\circ}+13^{\circ}\\\\\frac{4x}{5}=23^{\circ}\\\\ x=\frac{115}{4}{\circ}\\\\ x=28 \frac{3}{4}\\\\y=170^{\circ}-\frac{6\times 115}{5 \times 4}\\\\y=170^{\circ}-34.50^{\circ}\\\\y=135\frac{1}{2}^{\circ}\\\\z=180^{\circ}-y^{\circ}[/tex]

z=180°-(135.50)°

z=(44.50)°

[tex]z=44\frac{1}{2}^{\circ}[/tex]

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